Introduction to Options
Kerry Back
Options and Open Interest
A financial option is a right to buy or sell a financial security.
The right trades separately from the (underlying) security and usually even on a different exchange.
The rights are not (usually) issued by the companies who issue the underlying securities.
- Instead, the rights are created when someone buys one from someone else.
- Open interest is the number that exist at any time.
- Instead, the rights are created when someone buys one from someone else.
Example
- When a contract is first opened for trading, open interest is zero.
- Suppose Andy buys a contract from Chloe, and Brooke buys a contract from David.
- Longs = Andy and Brooke
- Shorts = Chloe and David
- Open interest = 2
- Suppose Andy then sells a contract to David.
- Andy: long + short = no position
- David: short + long = no position
- Longs = Brooke
- Shorts = Chloe
- Open interest = 1
Clearinghouse
- The long party has an option. The short party has an obligation.
- After a trade is made, the option clearinghouse steps in the middle and becomes the counterparty to both sides.
Hedging, speculation, and income
- You pay upfront to acquire an option.
- The amount you pay is called the option premium.
- It is not part of the contract but instead is determined in the market (like a stock price).
- The amount you pay is called the option premium.
- You buy options to hedge or to speculate. You sell options for income.
- Sellers of options need to have sufficient equity in their accounts (margin). A buyer needs enough cash to pay the premium but no more (like buying a stock).
Calls, puts, and strikes
A call option gives the holder the right to buy an asset at a pre-specified price.
A put option gives the holder the right to sell an asset at a pre-specified price.
The pre-specified price is called the exercise price or strike price.
American and European
An option is valid for a specified period of time, the end of which is called its expiration date or maturity date.
Most financial options can be exercised at any time the owner wishes, prior to maturity. Such options are called American.
There are some options that can only be exercised on the maturity date. They are called European. Both types are traded on both continents.
Moneyness
Borrowing language from horse racing, we say a call is
- in the money if the underlying price is above the strike,
- at the money if the underlying price equals the strike
- out of the money if the underlying price is below the strike
The reverse for puts
Also, “deep in the money” and “deep out of the money”
Value of a call at maturity
- At maturity, the value of a call is
\[\begin{cases} 0 & \text{if underlying < strike}\\ \text{underlying} - \text{strike} & \text{if underlying > strike} \end{cases} \]
- Equivalently, the value of a call is
\[\max(\text{underlying price}-\text{strike}, 0)\]
Value of a call at maturity
With strike = 50,
Value of a put at maturity
- At maturity, the value of a put is
\[\begin{cases} \text{strike} - \text{underlying} & \text{if underlying < strike}\\ 0 & \text{if underlying > strike} \end{cases} \]
- Equivalently, the value of a put is
\[\max(\text{strike}-\text{underlying price}, 0)\]
Value of a put at maturity
With strike = 50,